Representations and Characters of Finite Groups

Cambridge Studies in Advanced Mathematics #22

by M.J. Collins

Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced undergraduates that requires only a basic knowledge of group theory and general algebra. This theme is then expanded in a self-contained account providing an introduction to the application of character theory to the classification of simple groups. The book follows both strands of the the exceptional characteristics of Suzuki and Feit and the block character theory of Brauer and includes refinements of original proofs that have become available as the subject has grown.

256 pages, Paperback

First published March 22, 1990

Reviews

[Steve Dalton · Rating 2 out of 5]

This is a good book, but my major complaint is how bogged down in details it gets. I know this is a math book, but there are dozens of pages devoted to very specific examples, that I didn't find the least bit illuminating. There is definitely polish here; many of the proofs are concise and slick, without leaving too much out. And the exercises are challenging and thought-provoking. But by the time I got to the last section - on specific examples of exotic isometries - I almost wanted to stop reading. I would give this book a higher rating (4 stars) if some of these examples were cut out (and more general theory added in its place).

That said, this is one of the best sources for Glauberman's Z* theorem, without having to do (much) modular representation theory. Its proof is given in an appendix. I just wish that appendix wasn't the only reason I managed to finish the book.